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ISSN : 1226-0657

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Vol.15 No.4
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ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A C*-ALGEBRA

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.4, pp.393-400
An, Jong-Su
An,, J. (2008). ON AN ADDITIVE FUNCTIONAL INEQUALITY IN NORMED MODULES OVER A C*-ALGEBRA. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(4), 393-400.
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Abstract

In this paper, we investigate the following additive functional inequality (0.1) ||f(x)+f(y)+f(z)+f(w)||<TEX>${\leq}$</TEX>||f(x+y)+f(z+w)|| in normed modules over a <TEX>$C^*$</TEX>-algebra. This is applied to understand homomor-phisms in <TEX>$C^*$</TEX>-algebra. Moreover, we prove the generalized Hyers-Ulam stability of the functional inequality (0.2) ||f(x)+f(y)+f(z)f(w)||<TEX>${\leq}$</TEX>||f(x+y+z+w)||+<TEX>${\theta}||x||^p||y||^p||z||^p||w||^p$</TEX> in real Banach spaces, where <TEX>${\theta}$</TEX>, p are positive real numbers with <TEX>$4p{\neq}1$</TEX>.

keywords
Jordan-von Neumann functional equation, functional inequality, linear mapping in normed modules over a <tex> $C^*$</tex>-algebra

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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